It will probably be easier to have a failover profile setup in Ignition so you can still login. If you can’t authenticate against the database you can failover to an internal profile.
If you want to move the database from one machine to another it is easiest to just make a backup of those tables using the MySQL Workbench. It will create a .sql file that you can easily import into another database. The workbench will allow you to connect to both databases in the same program, making it easy to move from one to another.